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where

µ ¶
1
2
 =    +    −  Θ   +  0 
2
The amplitude  and the width ∆ are given by
0
r
3 8
 = and ∆ =  (4.13)
0 2
2  

with

2
 =  + 2   0 − 1 (4.14)


 0 is an arbitrary constant,   and   are the direction cosines of the wave

propagation with the  and  axes, respectively, and fulfill the condition
2
 +  =1 Also note that the product  ∆ =12  is independent of
2
2
2
  0 
 0 but depends on .

4.3 Results and Discussion

Dust acoustic soliton features in an unmagnetized dusty plasma having
Boltzmann distributed electrons, nonthermal ions, cold and hot adiabatic

dust grains have been studied. The application of the reductive perturba-

tion theory to the basic dust fluid equations leads to a nonlinear 3D-CKP
equation (4.11). In this study, the gravity force is neglected, on assuming

the dust radius    1 The mathematical results applied in F rings of

Saturn under the conditions: (i)   is smaller than 1, (ii) there are no
neutrals, (iii) the coupling parameter Γ  is less than unity, and (iv) the

ratio of inter-grain distances to Debye radius is less than one. Numerical

values corresponding to F-rings of Saturn have been used; the equilib-

rium dust and electron densities are  0 =10   0 =10   and dust
−3
−3

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